Kernel Density Estimation =========================== .. _kernel_density_notebook: `Link to Notebook GitHub `_ .. raw:: html
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import numpy as np
   from scipy import stats
   import statsmodels.api as sm
   import matplotlib.pyplot as plt
   from statsmodels.distributions.mixture_rvs import mixture_rvs

A univariate example.

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np.random.seed(12345)
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obs_dist1 = mixture_rvs([.25,.75], size=10000, dist=[stats.norm, stats.norm],
                   kwargs = (dict(loc=-1,scale=.5),dict(loc=1,scale=.5)))
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kde = sm.nonparametric.KDEUnivariate(obs_dist1)
   kde.fit()
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fig = plt.figure(figsize=(12,8))
   ax = fig.add_subplot(111)
   ax.hist(obs_dist1, bins=50, normed=True, color='red')
   ax.plot(kde.support, kde.density, lw=2, color='black');
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obs_dist2 = mixture_rvs([.25,.75], size=10000, dist=[stats.norm, stats.beta],
               kwargs = (dict(loc=-1,scale=.5),dict(loc=1,scale=1,args=(1,.5))))
   
   kde2 = sm.nonparametric.KDEUnivariate(obs_dist2)
   kde2.fit()
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fig = plt.figure(figsize=(12,8))
   ax = fig.add_subplot(111)
   ax.hist(obs_dist2, bins=50, normed=True, color='red')
   ax.plot(kde2.support, kde2.density, lw=2, color='black');

The fitted KDE object is a full non-parametric distribution.

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obs_dist3 = mixture_rvs([.25,.75], size=1000, dist=[stats.norm, stats.norm],
                   kwargs = (dict(loc=-1,scale=.5),dict(loc=1,scale=.5)))
   kde3 = sm.nonparametric.KDEUnivariate(obs_dist3)
   kde3.fit()
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kde3.entropy
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kde3.evaluate(-1)

CDF

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fig = plt.figure(figsize=(12,8))
   ax = fig.add_subplot(111)
   ax.plot(kde3.support, kde3.cdf);

Cumulative Hazard Function

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fig = plt.figure(figsize=(12,8))
   ax = fig.add_subplot(111)
   ax.plot(kde3.support, kde3.cumhazard);

Inverse CDF

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fig = plt.figure(figsize=(12,8))
   ax = fig.add_subplot(111)
   ax.plot(kde3.support, kde3.icdf);

Survival Function

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fig = plt.figure(figsize=(12,8))
   ax = fig.add_subplot(111)
   ax.plot(kde3.support, kde3.sf);